David Keogh, 50, who worked in Whitehall's communications centre, was jailed for six months at the Old Bailey for breaching the Official Secrets Act.
The researcher to whom he gave the memo, Leo O'Connor, was jailed for three months on a similar charge for passing the document to his employer, the anti-war Labour MP for Northampton South, Anthony Clarke.
The four-page memo recorded April 2004 Oval Office talks between the two leaders on events in the city of Falluja. Its contents were so secret that much of the trial was held behind closed doors with the press and public excluded.
The judge, Mr Justice Aikens, said Keogh's "reckless and irresponsible" actions could have cost British lives.
Ordering him to contribute £5,000 towards prosecution costs, Mr Aikens said Keogh, having been a civil servant for 25 years, was well aware of the terms of the Official Secrets Act.
"You decided that you did not like what you saw. Without consulting anyone, you decided on your own that it was in the best interest of the UK that this letter should be disclosed," he said.
"Your reckless and irresponsible action in disclosing this letter when you had no right to could have cost the lives of British citizens.
"This disclosure was a gross breach of trust of your position as a crown servant."
The judge told O'Connor that his actions could also have placed lives at risk.
After the sentencing, Keogh's solicitor, Stuart Jeffery, said the civil servant "took a moral stance on something that he found shocking" and said he would consider a possible appeal.
"It was never his intention to put lives at risk. He would state rather that it was his intention to save innocent lives," Mr Jeffery said. The trial centred around allegations that Keogh had leaked the document to O'Connor, who in turn left a copy in constituency papers for Mr Clarke in May 2004.
Keogh told the jury he wanted the memo to be used by MPs to ask questions in the House of Commons, and also to be seen by the 2004 US Democratic presidential candidate, John Kerry. However, when Mr Clarke found the memo he called the police.
The jury found the pair guilty yesterday after a trial in which government lawyers persuaded the judge that the jury could only hear the contents of the memo in private.
Mr Aikens made it clear he regarded the content as being so sensitive that the press could not report what Keogh said when he was asked in open court what preyed on his mind when he first saw the document.
Keogh was said to have described the contents as "abhorrent" and "illegal". According to O'Connor's statements to police, Keogh believed the memo exposed the US president as a "madman".
Though the defendants were arrested by police special branch officers soon after the document was handed to police, they were not charged until 18 months later, in November 2005.
Margaret Beckett, the foreign secretary, hinted that embarrassment was the real issue at stake when she signed a certificate for the court last year. She claimed the disclosure of the document would have a "serious negative impact" on UK-US diplomatic relations. "The ultimate consequence would be a substantial risk of harm to national security."
The prosecution admitted the leak did not contain any "actual damage", though it could have put British lives at risk. Martin Howard, a senior Ministry of Defence official, said any damage to British defence operations it might have caused was "short-lived".
The court heard that April 2004 was a particularly delicate period in Iraq. It is known, and was widely reported at the time, that British officials and military commanders were already expressing concern about US tactics. The British were concerned in particular about the US assault on Falluja, including the use of white phosphorous, which causes severe burns.
Peter Kilfoyle, the former defence minister, said yesterday: "There remain unanswered questions about the discussions [between Mr Blair and Mr Bush] about the attack on Falluja and the subsequent deaths of many hundreds of civilians."
British military chiefs at the time were urging Mr Blair to send extra forces only on British terms, not those of the US, whose tactics they privately damned as brutal and counterproductive.